Depending on where the numbness is, will determine what the nerve that is being compressed.

Ulnar nerve compression: If the numbness involves the pinky and ring finger then you are experiencing numbness from compression of the ulnar nerve where it goes underneath the heal portion of the palm of the hand on the pinky side. Treatment involves trying a different pair of padded gloves to decrease the pressure on that area. Specialize makes a pair of “Body Geometry” gloves with extra padding over the area of the ulnar nerve to help reduce this problem. Also using a slightly different back sweep of the handle bars may help by allow you hand to fall in a more neutral position. You will have to experiment here. I find that 5 degree back sweep works well with me. Others find that a 3 degree works and others still an 8 degree back sweep.

Median nerve compression: If the numbness goes to the thumb, index, middle and the ring finger along the side next to the middle finger, this is due to compression of the median nerve. This is called carpal tunnel syndrome as the median nerve passes through the "carpal tunnel" which is formed by the wrist (carpal) bones and the fibrous connecting tissue over laying these bones. This can be more serious as it can often be aggravated by daily work activities (repetitive use injury). Carpal tunnel syndrome can be aggravated by repetitive flexing and extending of the wrist which will occur when using twist type shifters (one of the few times I will recommend trigger type shifters). Carpal tunnel syndrome sometimes requires splinting of the wrist at night and sometimes during the day as well to prevent over flexing of the wrist during sleep or during work. Occasionally, carpal tunnel syndrome is severe enough to require medical intervention such as a local injection of anti-inflammatory steroids into the carpal tunnel or surgical release of the carpal tunnel.

For either of these maladies, you will benefit from a slightly taller stem to help decrease the amount of weight you are placing in your hands. Front suspension set up to a softer setting and/or a fatter front tire to mute the high frequency low impact vibrations can help as well. Using bar ends can help by allowing you to periodically reposition your hands to alleviate compression on the nerves in the hand and wrist. Develop a lighter grip on the handle bars to further reduce compression of the nerves.

If you have persistent or worsening numbness, pain or ANY weakness to you hands get an immediate medical evaluation.

I used to have issues with pain and numbness in the hands when riding.
Long story short, I rode the 64mile Ouachita Challenge mountain bike race in Arkansas last year and just about couldn't hold on even with my padded gloves and cork grips.
This year, I found a set of hand grips made by ERGON. I put them on and immediately, I could tell a difference. I used them in this year's 64 mile Ouachita Challenge and no hand pain/numbess issues as I previously experienced. The aches and pains were everywhere else though! www.ergon.com You will have to select the English version to translate the pages, unless you speak German.

REI sells them for about $30ish. Might be cheaper now.

The website goes into more detail, but the important points are the grips can be adjusted to keep your wrists straight and there is more surface area for your palms to rest on, which is padded with a type of rubber surface. The grips are easy to install. If you have SRAM grip-shift, I'm not sure if they would work. I use XT intergrated shifters and installed the grips with no problem.

They have different gender specific models.

My guess is you'll like them! Might add a little weight, but sure beats the alternative.